The finch beak: growth, form and function

Darwin's finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. Using 3D scans of skulls in this group, we perform an evolutionary morphometric analysis of the three-dimensional beak shapes and find that they can be fit by a simple functional form: the transverse sections of the beaks are parabolas with a curvature that decreases linearly with distance away from the tip of the beak. Guided by our morphometric analysis of finch beaks and earlier observations of the development of the zebra finch beak, we propose a minimal cellular and tissue level mechanism for beak morphogenesis that takes the form of a local geometric growth law. We show that this variant of curvature-driven flow captures the range of observed shapes of the finch beak in terms of two geometric parameters set by the size and shape of the developing beak bud. Finally we consider the role of beak orientation, along with its size and shape as determinants of its mechanical performance quantified in terms of the mechanical advantage of the beak treated as an elementary machine, and consider this in the context of the variable diets of finches.